Faithful Learning in Mathematics- The Paradox

By Nate Burchell (HS Mathematics Teacher)

In those seasons and moments when I have approached teaching as an act of worship, I have found richness and growth spiritually. I have grown to expect my work as a teacher to be deeply involved in my relationship with Christ. God speaks to us in the activities and relationships peculiar to our own days, a promised revelation in a native language. What have I learned as a mathematics teacher, what have I seen, how do I worship God? It’s complicated. I have accumulated a history of intimacy and experiences and anecdotes about God’s character that are difficult to explain to others, and that’s what a personal relationship is. We see God glorified and we treasure things in our hearts, pondering the design in those details. This is the unity and diversity of the body of Christ, that he reveals himself to us in so many personalized ways. This has been a big deal for me, the realization that the challenges and triumphs and setbacks of a consuming daily profession are ordained to teach me about my identity in Christ and to provide me with opportunities to honor Him.

I love that education involves a transformation of the mind. We need to actively cultivate a humility that will let us change our minds, and (simultaneously) the confidence and stability to resist such changes. We should be critical of new ideas, we should demand certainty, but we should be malleable and dynamic as well. In statistics a quantity called a significance level describes the delicate tension between our willingness to change our minds and our reluctance to do so. Wisdom involves a posturing of the mind that is neither gullible nor stubborn.

One of my favorite events in mathematics is the paradox. God spoke to Moses out of the paradox of a burning bush. Moses could have been the most jaded shepherd in the land, and he would still have been captivated by that impossible sight. Perhaps we are at our best as students when we have just been coaxed into muttering, “Wait a minute, how can this be?” So there is this paradox: that absurdity and confusion can play a critical role in the development of clear understanding.

I love watching students encounter those areas of math that entail such slippery ideas. In geometry, we require that everyone has the same understanding of “line”, yet the concept must remain undefined. In calculus, a limit relies on a quantity that is larger than zero but smaller than anything else. An infinite series can have a finite sum, and some have different sums according to the order in which you add the terms. As Christians, we embrace this paradox: an incomprehensible God who declares that he will be found by those who seek him. Maybe our occasional encounter with a paradox in math can help prepare us to recognize and embrace that thrill of backwards unexpected otherness we perceive in the message of the cross, which is foolishness to those who are perishing.